1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
|
*> \brief \b SQRT03
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE SQRT03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK,
* RWORK, RESULT )
*
* .. Scalar Arguments ..
* INTEGER K, LDA, LWORK, M, N
* ..
* .. Array Arguments ..
* REAL AF( LDA, * ), C( LDA, * ), CC( LDA, * ),
* $ Q( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ),
* $ WORK( LWORK )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SQRT03 tests SORMQR, which computes Q*C, Q'*C, C*Q or C*Q'.
*>
*> SQRT03 compares the results of a call to SORMQR with the results of
*> forming Q explicitly by a call to SORGQR and then performing matrix
*> multiplication by a call to SGEMM.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The order of the orthogonal matrix Q. M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of rows or columns of the matrix C; C is m-by-n if
*> Q is applied from the left, or n-by-m if Q is applied from
*> the right. N >= 0.
*> \endverbatim
*>
*> \param[in] K
*> \verbatim
*> K is INTEGER
*> The number of elementary reflectors whose product defines the
*> orthogonal matrix Q. M >= K >= 0.
*> \endverbatim
*>
*> \param[in] AF
*> \verbatim
*> AF is REAL array, dimension (LDA,N)
*> Details of the QR factorization of an m-by-n matrix, as
*> returned by SGEQRF. See SGEQRF for further details.
*> \endverbatim
*>
*> \param[out] C
*> \verbatim
*> C is REAL array, dimension (LDA,N)
*> \endverbatim
*>
*> \param[out] CC
*> \verbatim
*> CC is REAL array, dimension (LDA,N)
*> \endverbatim
*>
*> \param[out] Q
*> \verbatim
*> Q is REAL array, dimension (LDA,M)
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the arrays AF, C, CC, and Q.
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*> TAU is REAL array, dimension (min(M,N))
*> The scalar factors of the elementary reflectors corresponding
*> to the QR factorization in AF.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is REAL array, dimension (LWORK)
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> The length of WORK. LWORK must be at least M, and should be
*> M*NB, where NB is the blocksize for this environment.
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is REAL array, dimension (M)
*> \endverbatim
*>
*> \param[out] RESULT
*> \verbatim
*> RESULT is REAL array, dimension (4)
*> The test ratios compare two techniques for multiplying a
*> random matrix C by an m-by-m orthogonal matrix Q.
*> RESULT(1) = norm( Q*C - Q*C ) / ( M * norm(C) * EPS )
*> RESULT(2) = norm( C*Q - C*Q ) / ( M * norm(C) * EPS )
*> RESULT(3) = norm( Q'*C - Q'*C )/ ( M * norm(C) * EPS )
*> RESULT(4) = norm( C*Q' - C*Q' )/ ( M * norm(C) * EPS )
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup single_lin
*
* =====================================================================
SUBROUTINE SQRT03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK,
$ RWORK, RESULT )
*
* -- LAPACK test routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
INTEGER K, LDA, LWORK, M, N
* ..
* .. Array Arguments ..
REAL AF( LDA, * ), C( LDA, * ), CC( LDA, * ),
$ Q( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ),
$ WORK( LWORK )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ONE
PARAMETER ( ONE = 1.0E0 )
REAL ROGUE
PARAMETER ( ROGUE = -1.0E+10 )
* ..
* .. Local Scalars ..
CHARACTER SIDE, TRANS
INTEGER INFO, ISIDE, ITRANS, J, MC, NC
REAL CNORM, EPS, RESID
* ..
* .. External Functions ..
LOGICAL LSAME
REAL SLAMCH, SLANGE
EXTERNAL LSAME, SLAMCH, SLANGE
* ..
* .. External Subroutines ..
EXTERNAL SGEMM, SLACPY, SLARNV, SLASET, SORGQR, SORMQR
* ..
* .. Local Arrays ..
INTEGER ISEED( 4 )
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, REAL
* ..
* .. Scalars in Common ..
CHARACTER*32 SRNAMT
* ..
* .. Common blocks ..
COMMON / SRNAMC / SRNAMT
* ..
* .. Data statements ..
DATA ISEED / 1988, 1989, 1990, 1991 /
* ..
* .. Executable Statements ..
*
EPS = SLAMCH( 'Epsilon' )
*
* Copy the first k columns of the factorization to the array Q
*
CALL SLASET( 'Full', M, M, ROGUE, ROGUE, Q, LDA )
CALL SLACPY( 'Lower', M-1, K, AF( 2, 1 ), LDA, Q( 2, 1 ), LDA )
*
* Generate the m-by-m matrix Q
*
SRNAMT = 'SORGQR'
CALL SORGQR( M, M, K, Q, LDA, TAU, WORK, LWORK, INFO )
*
DO 30 ISIDE = 1, 2
IF( ISIDE.EQ.1 ) THEN
SIDE = 'L'
MC = M
NC = N
ELSE
SIDE = 'R'
MC = N
NC = M
END IF
*
* Generate MC by NC matrix C
*
DO 10 J = 1, NC
CALL SLARNV( 2, ISEED, MC, C( 1, J ) )
10 CONTINUE
CNORM = SLANGE( '1', MC, NC, C, LDA, RWORK )
IF( CNORM.EQ.0.0 )
$ CNORM = ONE
*
DO 20 ITRANS = 1, 2
IF( ITRANS.EQ.1 ) THEN
TRANS = 'N'
ELSE
TRANS = 'T'
END IF
*
* Copy C
*
CALL SLACPY( 'Full', MC, NC, C, LDA, CC, LDA )
*
* Apply Q or Q' to C
*
SRNAMT = 'SORMQR'
CALL SORMQR( SIDE, TRANS, MC, NC, K, AF, LDA, TAU, CC, LDA,
$ WORK, LWORK, INFO )
*
* Form explicit product and subtract
*
IF( LSAME( SIDE, 'L' ) ) THEN
CALL SGEMM( TRANS, 'No transpose', MC, NC, MC, -ONE, Q,
$ LDA, C, LDA, ONE, CC, LDA )
ELSE
CALL SGEMM( 'No transpose', TRANS, MC, NC, NC, -ONE, C,
$ LDA, Q, LDA, ONE, CC, LDA )
END IF
*
* Compute error in the difference
*
RESID = SLANGE( '1', MC, NC, CC, LDA, RWORK )
RESULT( ( ISIDE-1 )*2+ITRANS ) = RESID /
$ ( REAL( MAX( 1, M ) )*CNORM*EPS )
*
20 CONTINUE
30 CONTINUE
*
RETURN
*
* End of SQRT03
*
END
|
